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On maps with given Jacobians involving the heat equation

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Abstract

In this paper we present and analyze two new algorithms to construct a smooth diffeomorphism of a domain with prescribed jacobian function. The first one is free from any restriction on the boundary, while the second one produces a diffeomorphism that coincides with the identity map on the boundary of the domain. Both are based on the solution of an initial value problem for the linear heat equation, and the second also uses solutions of the Stokes system of Fluid Mechanics.

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Authors and Affiliations

  1. Departament de Matemàtica Aplicada 2, Universitat Politècnica de Catalunya, C. Pau Gargallo, 5, 08028, Barcelona, Spain

    Albert Avinyó

  2. Departament de Matemàtica Aplicada 1, Universitat Politècnica de Catalunya, Av. Diagonal, 647, 08028, Barcelona, Spain

    Joan Solà-Morales

  3. Departament de Matemàtica Aplicada 1, Universitat Politècnica de Catalunya, Av. Diagonal, 647, 08028, Barcelona, Spain

    Marta València

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  1. Albert Avinyó
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  2. Joan Solà-Morales
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  3. Marta València
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Correspondence to Albert Avinyó.

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Avinyó, A., Solà-Morales, J. & València, M. On maps with given Jacobians involving the heat equation . Z. angew. Math. Phys. 54, 919–936 (2003). https://doi.org/10.1007/s00033-003-0070-y

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  • DOI: https://doi.org/10.1007/s00033-003-0070-y

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